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Primel Length Units
The Primel Base Unit of Length: The ′lengthel (or ′kernel) The Primel base unit of length, the '''′lengthel''' (abbreviated ′Lgℓ), is derived by taking the product of the ′velocitel and the ′timel (which in turn is derived by taking the product of the ′accelerel and the ′timel). :: '''′lengthel''' = ′velocitel × ′timel = ′accelerel × ′timel2 This represents a distance traveled by an object moving at very close to 1 kilometer per hour over the course of 1 ′jiffy, i.e., 50/1728d of a second (0.042z s). The resulting length is a bit smaller than a centimeter: It is about 8.2d millimeters or about 0.3232d (0.3Ӿ67z in) (just slightly over 31/96d of an inch). In fact, it resembles an archaic English unit of measure known as the "barleycorn", which was exactly a third of an inch (0.400z in). Consequently, Primel proposes colloquializing this unit as the '''′kernel'''. It also happens to be a very close approximation for the line spacing of standard ruled paper. In the US, wide-ruled/legal-ruled paper spaces its lines 11/32d of an inch (0.416z in) apart. US medium-ruled/college-ruled paper spaces its lines 9/32d of an inch (0.376z in) apart. The ′lengthel is almost directly intermediate between these. This means that any standard notebook makes a fairly good approximation of a Primel ruler. You could use it to get a rough idea of how ordinary objects would be measured. For those accustomed to base units of length being at the scale of the USC foot or the SI meter, this may appear at first glance to be a rather small unit to serve as the basis for a system of measure. However, note that historically the centimeter itself actually served in such a role, as a foundation for the CGS (centimeter-gram-second) system, until that was supplanted by the MKS (meter-kilogram-second) system, now known as SI. The centimeter was, and still is, eminently serviceable as a unit of measure, and the ′lengthel is at least as serviceable. In fact, when we consider the ′lengthel together with its dozenal powers (as well as some simple multiples), they turn out to constitute a very useful suite of length units. Positive Dozenal Powers of the ′Lengthel The unqua′lengthel (or ′hand) The first positive dozenal power of the ′lengthel, the '''unqua′lengthel''' (abbreviated u↑′Lgℓ) is a dozen ′kernels. This is the distance traversed in a ′twinkling (a little over a third of a second) when moving at 1 ′velocitel. In SI units, this comes out to about 9.85d (9.Ӿ3z) centimeters, and therefore is very close to 1 decimeter. In USC units, it comes out to about 3.879d (3.Ӿ67z) inches, which is slightly more than 31/8d inches (3.Ӿ6z inches). This makes a good approximation for the USC "hand" unit, which is 4 USC inches. As a consequence, Primel proposes nicknaming this the '''′hand'''. The biqua′lengthel (or ′ell) The second dozenal power of the ′lengthel, the '''biqua′lengthel''' (abbreviated b↑′Lgℓ) is a dozen ′hands, or 100z ′kernels. This is the distance traversed in a ′waltzing (a little over 4 seconds) when moving at 1 ′velocitel. In SI units, this comes out to about 118.2d (9Ӿ.9z) centimeters, very close to a dozen decimeters. In USC units, it comes out to about 46.55d (3Ӿ.67z) inches. This makes a good approximation for the English "ell", an old unit of cloth measure, which was 45d (39z) inches. Consequently, Primel proposes to colloquialize this the '''′ell'''. The triqua′lengthel (or ′remulcum) Venturing beyond the "human-body" scale, the third dozenal power of the ′lengthel, the '''triqua′lengthel''' (abbreviated t↑′Lgℓ) is a dozen ′ells, or 100z ′hands, or 1000z ′kernels. This is the distance traversed in a ′brevit (50d (42z) seconds) when moving at 1 ′velocitel. In SI units, this comes out to about 14.187d (12.22Ӿz) meters. In USC units, this is about 46.55d (3Ӿ.67z) feet, or 15.52d (13.62z) yards. This length is very close to that of an intermodal shipping container, or a semi-trailer -- which can easily amount to the same thing, since a shipping container can often be mounted onto a semi-trailer bed. (Such vehicles are usually about 40d to 45d USC feet.) The French word for "trailer" or "towing" is ''remorque''. In Spanish and Galician, it is ''remolque''. In Catalan, ''remolc.'' In Portuguese ''reboque''. In Italian, ''rimorchio''. In Romanian, ''remorcă''. These words are cognate, because they all trace back to the Latin ''remulcum'', "towed". The Romans actually took this as a loan-word, from the Greek ''ῥῡμουλκέω'' (''rhymoulkeo'') "to tow", which itself was fused together from the phrase ''ῥῦμα ἕλκω'' (''rhyma helko''), which means "to drag" (''helko'') "a towing-line" (''rhyma'' = literally, "a thing drawn or pulled", as in a bowstring or a boat-line). Remarkably, the word survives in the Modern Greek phrase for a semi-trailer: ''ρυμουλκόμενο όχημα'' (''rymoulkomeno ochema'') "a towed vehicle". Primel will adopt the Latin version of this word, to make '''′remulcum''' the colloquialism for the triqua′lengthel. The quadqua′lengthel (or ′stadium) The fourth dozenal power of the ′lengthel, the '''quadqua′lengthel''' (abbreviated q↑′Lgℓ) is a dozen ′remulcums, or 100z ′ells, or 1000z ′hands, or 10,000z ′kernels. This is the distance traversed in a ′segment (10d (Ӿ) minutes) when moving at 1 ′velocitel. In SI units, this comes out to about 170.25d (122.3z) meters. In USC units, this is about 558.55d (3Ӿ6.67z) feet, or 186.18d (136.22z) yards. The nearest modern-day analog to this length that comes to mind is the furlong. However, at 660d (470z) feet, the furlong is a rather poor match: It comes out to about 1.22z quadqua′lengthels, more than a sixth too large; the quadqua′lengthel is only about 84.6%d (Ӿ1.Ӿ%z) of a furlong, almost a sixth too small. However, there is an ancient unit of measure that makes a rather better match: the Greek [http://en.wikipedia.org/wiki/Stadion_%28unit_of_length%29 ''stadion''] (''στάδιον''), Latinized as ''stadium'', and Anglicized as ''stade''. Herodotus defined the stadion as being 600d (420z) feet. However, different ancient Greek city-states had different definitions of the foot. Two prominent ones were the standard Attic/Alexandrian foot of about 308d milimeters, which would place the stadion at about 185d meters; and the Olympic foot (from the city-state of Olympia) of about 294d milimeters, which would place the stadion at about 176d meters. The quadqua′lengthel comes to about 92.0%d (Ɛ0.6%z) of the Attic stadion, and to about 96.7%d (Ɛ7.4%z) of the Olympic stadion. On the strength of this correspondence, Primel will use the Latin form of this word, to make the '''′stadium''' the colloquialization for the quadqua′lengthel. It still makes a good approximation for the size of most modern sports stadiums. The pentqua′lengthel (or ′dromicum) The fifth dozenal power of the ′lengthel, the '''pentqua′lengthel''' (abbreviated p↑′Lgℓ) is a dozen ′stadiums, or 100z ′remulcums, or 1000z ′ells, or 10,000z ′hands, or 100,000z ′kernels. This is the distance traversed in 1 ′stage of a day (2 hours) when moving at 1 ′velocitel. In SI units, this comes out to about 2042.96d (1222.Ɛ6z) meters, just slightly over 2 kilometers. In USC units, this is about 6702.62d (3Ӿ66.75z) feet. This makes the pentqua′lengthel a good unit for travel distances, on the order of the mile. However, at more than a quarter larger than a statute mile (1.269d mi), and more than 10%d larger even than a nautical mile (1.103d n.mi.), calling the pentqua′lengthel some kind of "mile" would not be a good fit. (See [#Auxiliary_Length_Units below] for a better mile analog.) The pentqua′lengthel is a new sort of unit that needs a new name coined for it. About 2 kilometers appears to have been a threshold distance for a "long race" in ancient Greece. For instance, the ''dolichus'' (''δόλιχος'') event in the ancient Olympics has been described by one source as being a dozen stadiums long, or about 2.2d kilometers (although most sources place it as being about a league, or 3 miles). The ancient Greek word for "race-course" or "running track" is ''dromos'' (δρόμος). Several modern words incorporate it: ''palindrome'', ''prodromal'', ''hippodrome'', ''velodrome'', ''aerodrome''. In modern Greek ''dromos'' has evolved into a simpler, and more generalized meaning of "road", in just about every sense that "road" has in English. That includes not only a simple ordinary street, but also a "road to" someplace, and even the metaphorical sense of one's "road" through life. The pentqua′lengthel is certainly quite serviceable as a unit for measuring travel distances "on the road". Consequently, Primel with use a Latinized form of this word, and colloquialize the pentqua′lengthel as the '''′dromicum'''. The hexqua′lengthel (or ′itinerum) The sixth dozenal power of the ′lengthel, the '''hexqua′lengthel''' (abbreviated h↑′Lgℓ) is a dozen ′dromicums, or 100z ′stadiums, or 1000z ′remulcums, or 10,000z ′ells, or 100,000z ′hands, or 1,000,000z ′kernels. This is the distance traversed in 1 day when moving at 1 ′velocitel. In SI units, this comes out to about 24.515d (20.623z) kilometers. In USC units, this is about 15.233d (13.297z) miles. This turns out to be a fair estimate of the distance a Roman legion could move in a day. In modern times, it also is about the threshold distance beyond which a commute to work by automobile is considered to be severely detrimental to one's quality of life (including apparently being linked to a greatly increased risk for obesity). The Latin word for "a day's march" was ''iter'' (genitive ''itineris''). From this we get the modern English words "itinerant" (someone who travels about), and "itinerary" (a travel schedule). Since the hexqua′lengthel appears to be conceptually linked to the concept of "daily travel", Primel proposes to colloquialize it as the '''′itinerum'''. The septqua′lengthel (or ′regionum) The seventh dozenal power of the ′lengthel, the '''septqua′lengthel''' (abbreviated s↑′Lgℓ) is a dozen ′itinerums, or 100z ′dromicums, or 10,000,000z ′kernels. An object moving at 1 ′velocitel it would take a dozen days to travel this distance. In SI units, this comes out to about 294.19d (206.23z) kilometers. In USC units, this is about 182.80d (132.97z) miles. Since this is a good size for measuring regional distances, Primel proposes nicknaming this unit the '''′regionum'''. The octqua′lengthel (or ′continentum) The eighth dozenal power of the ′lengthel, the '''octqua′lengthel''' (abbreviated o↑′Lgℓ) is a dozen ′regionums, or 100z ′itinerums, or 1000z ′dromicums, or 100,000,000z ′kernels. An object moving at 1 ′velocitel it would take a 100z days to travel this distance. In SI units, this comes out to about 3530.2d (2062.3z) kilometers. In USC units, this is about 2193.6d (1329.7z) miles. Since this is a good size for measuring continental distances, Primel proposes nicknaming this unit the '''′continentum'''. The ennqua′lengthel (or ′orbitum) The ninth dozenal power of the ′lengthel, the '''ennqua′lengthel''' (abbreviated e↑′Lgℓ) is a dozen ′continentums, or 100z regionums, or 1000z ′itinerums, or 10,000z ′dromicums, or 1,000,000,000z ′kernels. An object moving at 1 ′velocitel it would take a 1000z days to travel this distance. In SI units, this comes out to about 42,362.8d (20,622.9z) kilometers. In USC units, this is about 26,323d (13,297z) miles. This is somewhat more than the circumference of the Earth. If drawn as a circle around the Earth's center of mass, it would correspond to an orbit at an altitude of about 375d (273z) kilometers, which is right in the middle of the Low Earth Orbit range. If plotted as the radius of a circle drawn around the Earth's center, it be just slightly larger than the geostationary orbit. Accordingly, Primel proposes to nickname this unit the '''′orbitum'''. Correlation of Primel Length and Time Powers In summary, the ′velocitel can now be equated to: 1 ′orbitum per triquaday 1 ′continentum per biquaday 1 ′regionum per unquaday 1 ′itinerum per day 1 ′dromicum per ′stage 1 ′stadium per ′segment 1 ′remulcum per ′brevit 1 ′ell per ′waltzing 1 ′hand per ′twinkling 1 ′kernel per ′jiffy Auxiliary Length Units We can create an entire series of interesting auxiliary units that are all triples of the lengthel's various dozenal powers, as well as some additional multiples that are similarly noteworthy: The trina′lengthel (or ′thumb) If the ′lengthel approximates a third of an inch, then naturally 3 ′lengthels make a fair approximation of the inch itself. We can introduce this as an auxiliary unit called the '''trina′lengthel''' (abbreviated t•′Lgℓ). In USC units, this comes out to about 0.9697d (0.Ɛ778z) inches, which is slightly more than 31/32d of an inch (0.Ɛ76z inch). In SI units, it comes out to about 2.463d (2.568z) centimeters. This is quite close to the so-called "metric inch", defined as exactly 2.5d (2.6z) centimeters. That said, it would not be appropriate to nickname the trina′lengthel a "Primel inch". This is because the English word "inch" is derived from the Latin word ''uncia'', which meant exactly the same thing it now does in SDN: "a twelfth part"! The inch got that name because it is a twelfth part of the foot (Latin ''pes''). But in Primel terms, the trina′lengthel is not an "uncia" of its base unit, it is 3 base units. However, many languages use their word for "thumb" to mean "inch". For instance, the Latin word for "thumb" is ''pollex'', and the Romans used this word for the length unit as well. Consequently, Primel proposes colloquializing the trina′lengthel as the Primel '''′thumb'''. The trina-unqua′lengthel (or ′foot) A length of a dozen ′thumbs can be introduced as an auxiliary unit called the '''trina-unqua′lengthel''' (abbreviation t•u↑′Lgℓ). This is 3 ′hands, or 30z ′kernels. This makes a fair approximation of the USC foot, coming out to about 11.64d (Ɛ.778z) inches (slightly more than 11d 5/8 inches), or about 0.9697d (0.Ɛ778z) feet. In SI units, it comes out to about 29.6d (25.7z) centimeters, which is quite close to 30d (26z) centimeters, also known as the "metric foot". Consequently, Primel proposes nicknaming this the '''′foot'''. (Were it not for the difference between the TGM Gee and the Primel ′accelerel, the ′foot would be identical to the TGM Grafut.) The ennea-unqua′lengthel (or ′yard) Three ′feet, or 30z ′thumbs, can be introduced as an auxiliary unit called the '''ennea-unqua′lengthel''' (abbreviation e•u↑′Lgℓ). This is 9 ′hands, or 90z ′kernels. This makes a fair approximation of the USC yard, coming out to about 34.91d (2Ӿ.ӾƐz) inches, or about 2.909d (2.ӾӾƐz) feet, or about 0.9697d (0.Ɛ778z) yards. In SI units, it comes out to about 0.8867d (0.Ӿ782z) meters, which is quite close to 90d (76z) centimeters, which is three "metric feet". Consequently, Primel proposes nicknaming this the '''′yard'''. The undithexa-biqua′lengthel (or ′fathom) Two ′yards, or 6 ′feet, or 60z ′thumbs, can be introduced as an auxiliary unit called the '''undithexa-biqua′lengthel''' (abbreviation ′u•h•b↑′Lgℓ). This is 160z ′kernels, or 16z ′hands, or one and a half ′ells (and hence could also be called a '''sesqui-′ell''', or '''sesqui-biqua′lengthel'''). In SI units, this comes out to about 177.3d (129.4z) centimeters, or 1.773d (1.934z) meters. In USC units, this is about 68.9d (58.Ӿz inches), or 5.82d (5.9Ӿz) feet, or 1.94d (1.Ӿ3z) yards. This is a fair approximation (about 0.9697d (0.Ɛ778z)) of the nautical fathom, which is 6 USC feet. Consequently, Primel proposes to colloquialize this the '''′fathom'''. It also happens to be very close to the [http://en.wikipedia.org/wiki/Human_height#Average_height_around_the_world average height for males in the United States]. The trina-biqua′lengthel (or ′perticum) A dozen ′feet, or 100z ′thumbs, can be introduced as an auxiliary unit called the '''trina-biqua′lengthel''' (abbreviation t•b↑′Lgℓ). This is 3 ′ells, or 30z ′hands, or 300z ′kernels. In SI units, this comes out to about 3.547d (3.669z) meters. In USC units, this is about 139.6d (Ɛ7.78z) inches, or 11.64 (Ɛ.778) feet. The ancient Romans had a unit of measure called the ''pertica'' which was somewhere between 2.96d (2.Ӿ6z) and 3.05d (3.07z) meters, or about 10 (Ӿ) feet. The trina-biqual′engthel is about 1/6 to 1/5 larger than the Roman unit. However, in the Romance nations during the Medieval period, this unit evolved into several different lengths (some quite a bit larger), all variously known as a ''pertica'' or ''perch'' unit (and related to the Germanic ''rood'' or ''ruthe'' or English ''rod''). In Parma the ''pertica'' was as high as 3.25d (3.3z) meters. The trina-biqua′lengthel would be only about 9%d (11%z) larger than that. On the strength of this, Primel proposes to nickname this unit the '''′perticum'''. The trina-triqua′lengthel (or ′carinum) A dozen ′perticums, or 100z ′feet, can be introduced as an auxiliary unit called the '''trina-triqua′lengthel''' (abbreviation t•t↑′Lgℓ). This is ′3 remulcums, or ′30z ells, or 300z ′hands, or 3000z ′kernels. In SI units, this comes out to about 42.56d (36.69z) meters. This is equivalent to about 139.64d (Ɛ7.78z) USC feet. This is on the order of the size of modern [http://www.burgessyachts.com/en/sale-purchase-category/yachts-for-sale/sailing-yachts luxury sailing yachts]. The Latin word for "keel" is ''carina''. Consequently, Primel proposes giving the nickname '''′carinum''' to the trina-triqua′lengthel. The trina-quadqua′lengthel (or ′trientum) A dozen ′carinums, or 1000z ′feet, can be introduced as an auxiliary unit called the '''trina-quadqua′lengthel''' (abbreviation t•q↑′Lgℓ). This is ′3 stadiums, or 300z ells, or 3000z ′hands, or 30,000z ′kernels, or a quarter of a ′dromicum. In SI units, this comes out to about 510.7d (366.9z) meters. This is equivalent to about 1675.7d (Ɛ77.8z) USC feet, or 0.3173d (0.3984z) statute miles. Since this is a bit less than a third of a mile, Primel proposes colloquializing this as the '''′trientum''', from the Latin word for "one third", ''triens''. The hexa-quadqua′lengthel (or ′besum) Two ′trientums, or 2000z ′feet, can be introduced as an auxiliary unit called the '''′hexa-quadqua′lengthel''' (abbreviation h•q↑′Lgℓ). This is 6 ′stadiums, or 600z ′ells, or 6000z ′hands, or 60,000z ′kernels, or half a ′dromicum. In SI units this comes out to about 1021.5d (711.6z) meters, just slightly over 1 kilometer. One possible colloquialism this suggests is to call this unit a '''′kay''', after a common colloquialism for the kilometer. However, in USC units this length is about 3351.3d (1Ɛ33.3z) feet, or about 0.6347d (0.774Ӿz) statute miles. This is just under two-thirds of a mile. Since the ancient Latin word for "two-thirds" is ''bes'', Primel also proposes the colloquialism '''′besum''' for this length. The ennea-quadqua′lengthel (or ′milum) Three ′trientums, or 3000z ′feet, can be introduced as an auxiliary unit called the '''ennea-quadqua′lengthel''' (abbreviation e•q↑′Lgℓ). This is 9 ′stadiums, or 900z ′ells, or 9000z ′hands, or 90,000z ′kernels, or three-quarters of a ′dromicum. In SI units this comes out to about 1532.2d (Ӿ78.2z) meters, just slightly over a kilometer and a half. In USC units this length is about 5027.0d (2ӾӾƐ.0z) feet, or about 0.9521d (0.Ɛ512z) statute miles. This a very close approximation of a customary mile (much closer than the ′dromicum). On the strength of this, Primel proposes colloquializing this length as a '''′milum'''. The trina-pentqua′lengthel (or ′parasang) A dozen ′trientums, or 10,000z ′feet, can be introduced as an auxiliary unit called the '''trina-pentqua′lengthel''' (abbreviation ′3PLgℓ). This is 3 ′dromicums, or 3000z ′ells, or 30,000z ′hands, or 300,000z ′kernels. In SI units, this comes out to about 6128.9d (3668.Ӿz) meters. This is equivalent to about 20107.9d (Ɛ777.Ӿz) USC feet, or about 3.808d (3.984z) statute miles. Traditionally, 3 customary miles (statute or nautical) has been called a "league". The ′dromicum is the Prime dozenal power closest to the customary mile, and therefore likely to be the preferred measure of travel distances in a Primel world, playing the role of a Primel "mile-analog". Since the trina-pentqua′lengthel is three ′dromicums, one might be tempted to colloquialize this as a "Primel league." But just as the ′dromicum is a bit too outsized to match the customary mile, so too the ′tridromicum is a bit too large to match the customary league. (The ennea-quadqua′lengthel, or ′milium, makes a much closer "Primel mile", so the bidittri-pentqua′lengthel (230,000z ′lengthels) would make a better "Primel league." However, there is an ancient unit of measure that might fit the bill much better: the Persian ''parasang''. The trouble is, Western scholars of Persian antiquity are all over the map in their assessment of exactly how long the ''parasang'' actually was. Herodotus quoted a figure of 30d (26z) ancient Greek stadia, which certainly gets it into the ballpark. But other sources have claimed it was closer to 40d (34z) stadia, or even longer. Certainly a length of 36d (30z) stadia is not out of the question. However, ''modern'' Persia has weighed in on this, and has officially established a ''standardized metric version'' of the parasang (in contemporary Farsi, a ''farsang''), defined to be exactly 6 SI kilometers (or about 3.8d customary miles). Certainly if anyone can be trusted to provide a conclusive definition of what the ancient parasang must have been, modern Persians would be the experts! Six kilometers is an extraordinarily close match to the trina-pentqua′lengthel. On the strength of this, Primel proposes nicknaming this unit the '''′parasang'''. Table of Primel Length Units and Their Conversions to SI and USC